An irrational number cannot be fully written down in decimal form. It would have an infinite number of digits after the decimal point. These digits would also not repeat.

√2 is irrational

Irrational numbers often occur in geometry. For instance, if we have a square which has sides of 1 meter, the distance between opposite corners is the square root of two meters. This is an irrational number. In decimal for it is written as 1.414213... Mathematicians have proved that the square root of every natural number is either an integer or an irrational number.

One well known irrational number is pi. This is the circumference of a circle divided by its diameter. This number is the same for every circle. The number pi is approximately 3.14159265358979323… .